Abstract
The yield function is very important in establishing the plastic constitutive relation and analyzing the plastic deformation. Hence, expanded on the general yield function in its Taylor to six-order plastic tensors, this article gives a new yield function on isotropic metal. Based on independent properties of the hydrostatic pressure for metal yield, such as derivation character, mechanical property invariance of isotropic metal etc ., these plastic tensors are analyzed as traceless, totally symmetric and objective. And the yield function for isotropic metals can be degenerated to the one for identical and different property of tension-compression yield. Finally, by means of the results of Lode test, it is proved that the new yield function is quite suitable for those metal materials having both the identical and different properties of tensioncompression yield. There are many merits of this yield function, such as it includes only 2 parameters for material, i.e. simple form and generality etc . And this yield function will lay a theoretical foundation for analyzing mechanical properties of metal materials.
Highlights
The yield function is vital and necessary to describe the plastic deformation of metal
Based on the results of simple tension test for mild steel, Tresca yield function is shown in Eq 1
Based on the stress relation, the general form of a new yield function included the various degree terms for one from three on the isotropic metals and corresponding sixorder plastic tensor was deduced in this thesis; A new yield function of the isotropic metals is derived from the isotropic plastic tensor based on the total symmetries, traceless, objectivity and isotropy
Summary
The yield function is vital and necessary to describe the plastic deformation of metal. There are hundreds of yield functions of metal, such as functions suggested by Hill, Hershey, Balart, Hosford, Man C.-S and Huang et al, to precisely describe the mechanical behavior of metals [12]. Based on the results of simple tension test for mild steel, Tresca yield function is shown in Eq 1. This function is simple, since it doesn’t consider the second principal stress. Considering the second principal stress, Von-mises yield function, Eq (2), is derived from the results of simple tension. Simple uniaxial tensioncompression experiment can be used to determine the parameters
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